During the Clone Wars, Anakin is a Jedi Knight and has his own Padawan (Ahsoka).
Why didn't Obi-Wan take another Padawan apprentice?
Obi-Wan is on the Jedi Council, and thus no longer has an apprentice. We don't see any other member of the Council (Yoda, Windu, Ki-Adi-Mundi, etc.) with Padawans. They may teach Younglings in a class (as we see Yoda doing), but are no longer focused on ONE trainee. They are concerned with all Jedi, and the Republic as a whole, at that point.
Depa Billaba training Kanan Jarrus is a notable exception, but we only find that out after Star Wars Rebels was released. Since she didn't get much screen time in the movies, we can assume the restriction only applied to senior members of the Jedi Council.
The very short answer is that it was because it wasn't the will of the Jedi Council. At the start of the Clone Wars film, we learn that Kenobi did indeed discuss (with Yoda) the possibility of getting a new Padawan learner. Ahsoka Tano was sent, but in a surprise move Yoda assigned her to Anakin Skywalker rather than Kenobi.
The clear implication seems to be that Obi-Wan wasn't assigned a new Padawan because he was expected to keep an eye on the both of them.
On at least one occasion, Yoda threatened to transfer her guardianship to Obi-wan, something that wouldn't be a possibility if he was encumbered with his own learner